Question 1

A tennis ball bounces on the floor three times,and each time it loses 23.0% of its energy due to heating.How high does it bounce after the third time,if we released it 
From the floor?

Accepted Answer

The answer of A tennis ball bounces on the floor...

Question 2

A spring-loaded dart gun is used to shoot a dart straight up into the air,and the dart reaches a maximum height of 24 meters.The same dart is shot up a second time from the same gun,but this time the spring is compressed only half as far (compared to the first shot).How far up does the dart go this time (neglect all friction and assume the spring is ideal)?

Accepted Answer

The answer of A spring-loaded dart gun is used to...

Question 3

A prankster drops a water balloon from the top of a building.If the balloon is traveling at 29.1 m/s when it strikes a window ledge that is 1.5 m above the ground,how tall is the building? Neglect air resistance.

Accepted Answer

Using the kinematic equation $ v^2 = u^2 + 2as $, where $ v = 29.1 \, \text{m/s} $, $ u = 0 \, \text{m/s} $, $ a = 9.8 \, \text{m/s}^2 $, and $ s $ is the distance fallen. Solving for $ s $ gives approximately 43 m. Adding the 1.5 m above the ground, the building is about 45 m tall.

Question 4

An ideal spring with a force constant (spring constant)of 15 N/m is initially compressed by 3.0 cm from its uncompressed position.How much work is required to compress the spring an additional 4.0 cm?

Accepted Answer

The answer of An ideal spring with a force constant...

Question 5

A 5.0-N projectile leaves the ground with a kinetic energy of 220 J.At the highest point in its trajectory,its kinetic energy is 120 J.To what vertical height,relative to its launch point,did it rise if there was no air resistance?

Accepted Answer

The answer of A 5.0-N projectile leaves the ground with...

Question 6

An ideal spring has a spring constant (force constant)of 60 N/m.How much energy does it store when it is stretched by 1.0 cm?

Accepted Answer

The energy stored in a spring is given by the formula $E = \frac{1}{2}kx^2$, where $E$ is the energy in joules, $k$ is the spring constant in N/m, and $x$ is the displacement in meters. Here, $k = 60$ N/m and $x = 1.0$ cm = 0.01 m. Plugging these values into the formula gives $E = \frac{1}{2} \times 60 \times (0.01)^2 = 0.003$ J.

Question 7

A toy rocket that weighs 10 N blasts straight up from ground level with an initial kinetic energy of 40 J.At the exact top of its trajectory,its total mechanical energy is 140 J.To what vertical height above the ground does it rise,assuming no air resistance?

Accepted Answer

The answer of A toy rocket that weighs 10 N...

Question 8

A bead is moving with a speed of 20 m/s at position A on the track shown in the figure.This track is friction-free,and there is no appreciable air resistance.What is the speed of the bead at point C?

Accepted Answer

The answer of A bead is moving with a speed...

Question 9

An ideal spring with a spring constant (force constant)of 
Is stretched from equilibrium to 2.9 m.How much work is done in the process?

Accepted Answer

The answer of An ideal spring with a spring constant...

Question 10

The figure shows a famous roller coaster ride.You can ignore friction.If the roller coaster leaves point Q from rest,what is its speed at the top of the 25-m peak (point S)?

Accepted Answer

At point Q, the roller coaster has potential energy (mgh), where m is the mass of the roller coaster, g is the acceleration due to gravity, and h is the height of point Q above the ground. When the roller coaster reaches the top of point S, all of its potential energy has been converted to kinetic energy (1/2 mv^2), where v is the speed of the roller coaster. Therefore, we can use the conservation of energy to solve for v:

mgh = 1/2 mv^2

Canceling the mass and multiplying both sides by 2, we get:

2gh = v^2

Plugging in the values, we get:

2(9.8 m/s^2)(25 m) = v^2

Simplifying, we get:

v = 22.14 m/s

So, the speed of the roller coaster at the top of point S is approximately 22 m/s, which is closest to choice B.

Question 11

If the work done to stretch an ideal spring by 4.0 cm is 6.0 J,what is the spring constant (force constant)of this spring?

Accepted Answer

The formula for the potential energy stored in a spring is: 
PE = (1/2)kx^2 
where k is the spring constant and x is the displacement from equilibrium.

Given: 
PE = 6.0 J 
x = 4.0 cm = 0.04 m

Substituting the values, 
6.0 = (1/2)k(0.04)^2 
k = 7500 N/m

Therefore, the spring constant is 7500 N/m. Choice D is the correct answer.

Question 12

How much work is required to stretch an ideal spring of spring constant (force constant)40 N/m from x = 0.20 m to x = 0.25 m if the unstretched position is at x = 0.00 m?

Accepted Answer

The work done to stretch a spring is given by the formula: 
W = (1/2)k(x2^2 - x1^2) 
where k is the force constant, x1 is the initial displacement, and x2 is the final displacement. 
Here, k = 40 N/m, x1 = 0.20 m, and x2 = 0.25 m. 
Therefore, 
W = (1/2)(40 N/m)((0.25 m)^2 - (0.20 m)^2) 
W = 0.45 J 
Thus, the work required to stretch the spring from x = 0.20 m to x = 0.25 m is 0.45 J, which corresponds to choice A.

Question 13

A 60-kg skier pushes off the top of a frictionless hill with an initial speed of 4.0 m/s.How fast will she be moving after dropping 10 m in elevation? Air resistance is negligible.

Accepted Answer

To solve this problem, we use the principle of conservation of mechanical energy, which states that the total mechanical energy (kinetic energy + potential energy) in a system remains constant if only conservative forces are doing work. The skier's initial kinetic energy plus her initial potential energy equals her final kinetic energy (since her final potential energy at the bottom is zero in this context). The equation for kinetic energy is $KE = \frac{1}{2}mv^2$ and for potential energy is $PE = mgh$, where $m$ is mass, $v$ is velocity, $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$), and $h$ is height.Initial kinetic energy: $KE_i = \frac{1}{2} \times 60 \times (4)^2 = 480 J$Initial potential energy: $PE_i = 60 \times 9.8 \times 10 = 5880 J$Total initial energy: $E_i = KE_i + PE_i = 480 J + 5880 J = 6360 J$At the bottom, all this energy is converted into kinetic energy:$6360 J = \frac{1}{2} \times 60 \times v^2$Solving for $v$, we find:$v^2 = \frac{6360 \times 2}{60}$$v^2 = 212$$v = \sqrt{212} \approx 14.56 m/s$Rounding to the nearest whole number gives us approximately 15 m/s.

Question 14

Assuming negligible friction,what spring constant (force constant)would be needed by the spring in a "B-B gun" to fire a 10-g pellet to a height of 100 m if the spring is initially compressed by 0.10 m?

Accepted Answer

To find the spring constant (k), we use energy conservation principles. The potential energy stored in the spring (1/2 k x^2) when compressed is converted into gravitational potential energy (mgh) at the peak of the pellet's trajectory. Given: m = 0.01 kg (10 g converted to kg), g = 9.8 m/s^2 (acceleration due to gravity), h = 100 m, and x = 0.10 m. Rearranging the energy conservation equation 1/2 k x^2 = mgh for k gives k = 2mgh / x^2. Plugging in the values gives k = 2*0.01*9.8*100 / 0.10^2 = 1960 N/m, which when converted to N/cm (by dividing by 100) gives 19.6 N/cm, rounding to 20 N/cm.

Question 15

If 4.0 J of work are performed in stretching an ideal spring with a spring constant (force constant)of 2500 N/m,by what distance is the spring stretched?

Accepted Answer

The work done on a spring is given by the formula W = 0.5 * k * x^2, where W is the work done, k is the spring constant, and x is the distance stretched. Solving for x, we get x = sqrt(2W/k). Substituting W = 4.0 J and k = 2500 N/m, we find x = sqrt(2*4.0/2500) = 0.057 m = 5.7 cm.

Question 16

What is the minimum energy needed to lift a 1.0-kg rocket to a height of 200 km and to give it a speed of 8.0 km/s at that height? (Neglect air resistance and the small decrease in g over that distance. )

Accepted Answer

The minimum energy needed includes both the gravitational potential energy to lift the rocket to 200 km and the kinetic energy to give it a speed of 8.0 km/s. Calculating these gives approximately 34 MJ.

Question 17

A rock falls from a vertical cliff that is 4.0 m tall and experiences no significant air resistance as it falls.At what speed will its gravitational potential energy (relative to the base of the cliff)be equal to its kinetic energy?

Accepted Answer

The gravitational potential energy of the rock at the top of the cliff is given by:
PE = mgh
where m = mass of the rock, g = acceleration due to gravity, and h = height of the cliff.
At the base of the cliff, all the potential energy is converted into kinetic energy, given by:
KE = (1/2)mv^2
where v = speed of the rock.
At the point where PE = KE, we have:
mgh = (1/2)mv^2
Simplifying, we get:
v = sqrt(2gh)
Substituting the given values, we get:
v = sqrt(2 x 9.81 x 4.0) = 6.3 m/s
Therefore, the correct answer is C) 6.3 m/s.

Question 18

If a spring-operated gun can shoot a pellet to a maximum height of 100 m on Earth,how high could the pellet rise if fired on the Moon,where g = 1.6 m/s²?

Accepted Answer

The maximum height is inversely proportional to the gravitational acceleration. Since the Moon's gravity is 1/6th of Earth's, the pellet will rise 6 times higher, so 100 m * 6 = 600 m, which is closest to 610 m.

Question 19

A block slides down a frictionless inclined ramp and experiences no significant air resistance.If the ramp angle is 17.0° above the horizontal and the length of the surface of the ramp is 
Find the speed of the block as it reaches the bottom of the ramp,assuming it started sliding from rest at the top.

Accepted Answer

The answer of A block slides down a frictionless inclined...

Question 20

It takes 87 J of work to stretch an ideal spring from 1.4 m to 2.9 m from equilibrium.What is the value of the spring constant (force constant)of this spring?

Accepted Answer

The answer of It takes 87 J of work to...

Quiz 8: Potential Energy and Conservation of Energy

A tennis ball bounces on the floor three times,and each time it loses 23.0% of its energy due to heating.How high does it bounce after the third time,if we released it From the floor?

A prankster drops a water balloon from the top of a building.If the balloon is traveling at 29.1 m/s when it strikes a window ledge that is 1.5 m above the ground,how tall is the building? Neglect air resistance.

An ideal spring with a force constant (spring constant) of 15 N/m is initially compressed by 3.0 cm from its uncompressed position.How much work is required to compress the spring an additional 4.0 cm?

A 5.0-N projectile leaves the ground with a kinetic energy of 220 J.At the highest point in its trajectory,its kinetic energy is 120 J.To what vertical height,relative to its launch point,did it rise if there was no air resistance?

An ideal spring has a spring constant (force constant) of 60 N/m.How much energy does it store when it is stretched by 1.0 cm?

A toy rocket that weighs 10 N blasts straight up from ground level with an initial kinetic energy of 40 J.At the exact top of its trajectory,its total mechanical energy is 140 J.To what vertical height above the ground does it rise,assuming no air resistance?

A bead is moving with a speed of 20 m/s at position A on the track shown in the figure.This track is friction-free,and there is no appreciable air resistance.What is the speed of the bead at point C?

An ideal spring with a spring constant (force constant) of Is stretched from equilibrium to 2.9 m.How much work is done in the process?

The figure shows a famous roller coaster ride.You can ignore friction.If the roller coaster leaves point Q from rest,what is its speed at the top of the 25-m peak (point S) ?

If the work done to stretch an ideal spring by 4.0 cm is 6.0 J,what is the spring constant (force constant) of this spring?

How much work is required to stretch an ideal spring of spring constant (force constant) 40 N/m from x = 0.20 m to x = 0.25 m if the unstretched position is at x = 0.00 m?

A 60-kg skier pushes off the top of a frictionless hill with an initial speed of 4.0 m/s.How fast will she be moving after dropping 10 m in elevation? Air resistance is negligible.

Assuming negligible friction,what spring constant (force constant) would be needed by the spring in a "B-B gun" to fire a 10-g pellet to a height of 100 m if the spring is initially compressed by 0.10 m?

If 4.0 J of work are performed in stretching an ideal spring with a spring constant (force constant) of 2500 N/m,by what distance is the spring stretched?

What is the minimum energy needed to lift a 1.0-kg rocket to a height of 200 km and to give it a speed of 8.0 km/s at that height? (Neglect air resistance and the small decrease in g over that distance. )

A rock falls from a vertical cliff that is 4.0 m tall and experiences no significant air resistance as it falls.At what speed will its gravitational potential energy (relative to the base of the cliff) be equal to its kinetic energy?

If a spring-operated gun can shoot a pellet to a maximum height of 100 m on Earth,how high could the pellet rise if fired on the Moon,where g = 1.6 m/s²?

It takes 87 J of work to stretch an ideal spring from 1.4 m to 2.9 m from equilibrium.What is the value of the spring constant (force constant) of this spring?

Quiz 8: Potential Energy and Conservation of Energy

A tennis ball bounces on the floor three times,and each time it loses 23.0% of its energy due to heating.How high does it bounce after the third time,if we released it From the floor?

A prankster drops a water balloon from the top of a building.If the balloon is traveling at 29.1 m/s when it strikes a window ledge that is 1.5 m above the ground,how tall is the building? Neglect air resistance.

An ideal spring with a force constant (spring constant) of 15 N/m is initially compressed by 3.0 cm from its uncompressed position.How much work is required to compress the spring an additional 4.0 cm?

A 5.0-N projectile leaves the ground with a kinetic energy of 220 J.At the highest point in its trajectory,its kinetic energy is 120 J.To what vertical height,relative to its launch point,did it rise if there was no air resistance?

An ideal spring has a spring constant (force constant) of 60 N/m.How much energy does it store when it is stretched by 1.0 cm?

A toy rocket that weighs 10 N blasts straight up from ground level with an initial kinetic energy of 40 J.At the exact top of its trajectory,its total mechanical energy is 140 J.To what vertical height above the ground does it rise,assuming no air resistance?

A bead is moving with a speed of 20 m/s at position A on the track shown in the figure.This track is friction-free,and there is no appreciable air resistance.What is the speed of the bead at point C?

An ideal spring with a spring constant (force constant) of Is stretched from equilibrium to 2.9 m.How much work is done in the process?

The figure shows a famous roller coaster ride.You can ignore friction.If the roller coaster leaves point Q from rest,what is its speed at the top of the 25-m peak (point S) ?

If the work done to stretch an ideal spring by 4.0 cm is 6.0 J,what is the spring constant (force constant) of this spring?

How much work is required to stretch an ideal spring of spring constant (force constant) 40 N/m from x = 0.20 m to x = 0.25 m if the unstretched position is at x = 0.00 m?

A 60-kg skier pushes off the top of a frictionless hill with an initial speed of 4.0 m/s.How fast will she be moving after dropping 10 m in elevation? Air resistance is negligible.

Assuming negligible friction,what spring constant (force constant) would be needed by the spring in a "B-B gun" to fire a 10-g pellet to a height of 100 m if the spring is initially compressed by 0.10 m?

If 4.0 J of work are performed in stretching an ideal spring with a spring constant (force constant) of 2500 N/m,by what distance is the spring stretched?

What is the minimum energy needed to lift a 1.0-kg rocket to a height of 200 km and to give it a speed of 8.0 km/s at that height? (Neglect air resistance and the small decrease in g over that distance. )

A rock falls from a vertical cliff that is 4.0 m tall and experiences no significant air resistance as it falls.At what speed will its gravitational potential energy (relative to the base of the cliff) be equal to its kinetic energy?

If a spring-operated gun can shoot a pellet to a maximum height of 100 m on Earth,how high could the pellet rise if fired on the Moon,where g = 1.6 m/s2?

It takes 87 J of work to stretch an ideal spring from 1.4 m to 2.9 m from equilibrium.What is the value of the spring constant (force constant) of this spring?

If a spring-operated gun can shoot a pellet to a maximum height of 100 m on Earth,how high could the pellet rise if fired on the Moon,where g = 1.6 m/s²?